Power series question

We just started power series in class and I'm somewhat confused about them. I'm stuck on this particular problem. It says to make a power series for f(x) = x/(2x^2+1). What I did was to base it on geometric series so I convered the equation to look like 1/(1+x) so now it looks like x/[1-(-2x^2)]. What I got for the power series was x multiplied by the sum of (-2x^2)^n from n=0 to infinity. Is this right?